Secondary data analysis – meaning, in the broadest sense, analysis of data collected by someone else – plays a vital role in modern epidemiology and public health research and practice. This is partly because of the emphasis on population-based studies that is common to both fields. For instance, few individual researchers could hope to collect data sufficient to evaluate changes in the health status or health behaviors on a national scale. Fortunately, a wealth of data on health and related subjects, collected on a broad scale and over many years, is available for public use. However, locating secondary data appropriate to address a particular research question is not always easy, partly because an abundance of data is available and also because those data were collected by many different entities and are stored in many different locations. My primary purpose in writing Secondary Data Sources for Public Health is to facilitate use of those data sets in epidemiologic and public health research.

Chapter 1 introduces the topic of secondary data analysis, discusses some of its advantages and disadvantages, describes a general process for locating appropriate data to address a research question, and suggests some types of information that the researcher should try to acquire about any secondary data set being considered for analysis. Chapters 2 through 7 discuss the major secondary data sets and data archives available for studying health issues in the United States.

This chapter discusses a number of data sources that may be of interest to the epidemiologist and public health researcher, although they are not focused exclusively on health issues. The U.S. Census is the basic source of demographic information about people living in the United States and is often used by health researchers to provide contextual information such as the racial makeup or economic status of geographic areas they are studying. The Area Resource File (ARF) contains health, economic, and demographic information drawn from a number of sources and aggregated at the county level. It is also frequently used to provide contextual information for geographic areas. The General Social Survey (GSS) is a telephone survey conducted since 1972 that collects data on a variety of social issues, including alcohol and drug use, sexual behavior, and attitudes toward health issues such as abortion and euthanasia. The ICPSR, located at the University of Michigan, is a repository of data on a variety of topics, many of which are health related, including data from the Health and Medical Care Archive (HMCA) of the Robert Wood Johnson Foundation (RWJF). The Henry A. Murray Research Archive, housed at Harvard University, contains data and ancillary materials from more than 270 longitudinal studies of human development and social change. The Project on Human Development in Chicago Neighborhoods (PHDCN) is a large-scale, longitudinal study of how child and adolescent development is affected by families, schools, and neighborhoods.

What Are Secondary Data?

In the fields of epidemiology and public health, the distinction between primary and secondary data depends on the relationship between the person or research team who collected a data set and the person who is analyzing it. This is an important concept because the same data set could be primary data in one analysis and secondary data in another. If the data set in question was collected by the researcher (or a team of which the researcher is a part) for the specific purpose or analysis under consideration, it is primary data. If it was collected by someone else for some other purpose, it is secondary data. Of course, there will always be cases in which this distinction is less clear, but it may be useful to conceptualize primary and secondary data by considering two extreme cases. In the first, which is an example of primary data, a research team conceives of and develops a research project, collects data designed to address specific questions posed by the project, and performs and publishes their own analyses of the data they have collected. In this case, the people involved in analyzing the data have some involvement in, or at least familiarity with, the research design and data collection process, and the data were collected to answer the questions examined in the analysis.

This chapter discusses five surveys that gather information on multiple health-related topics. The National Health Examination Surveys (NHES) and its continuation, the National Health and Nutrition Examination Survey (NHANES), have been conducted periodically since 1960 and collect data on a wide variety of health topics through personal interview and direct physical examination. The National Health Interview Survey (NHIS) has been conducted annually since 1957 and gathers information through personal interviews with members of a representative sample of American households. The Joint Canada/United States Survey of Health (JCUSH) was conducted in 2002 to 2003, with a random sample of adults age 18 and older in Canada and the United States, was the first survey to collect comprehensive information about health and health care access in both countries. The Longitudinal Studies of Aging (LSOAs) consist of four surveys designed to study longitudinal changes in the health, functional status, living arrangements, and health services of older Americans as they age; the LSOAs were begun in 1984, and data were most recently collected in 2000. The State and Local Area Integrated Telephone Survey (SLAITS) is a data collection mechanism that has been used to conduct a number of different health-related surveys at the national, state, and local levels since 1997.

The National Health Examination Survey and the National Health and Nutrition Examination Survey

The NHES and the NHANES form part of an ongoing effort to collect data on illness and disability in the United States.

Medicare and Medicaid are U.S. governmental health insurance programs administered by the Centers for Medicare and Medicaid Services (CMS), formerly known as the Health Care Financing Administration. Both programs were signed into law on July 30, 1965, by President Lyndon B. Johnson. Medicare is a federal health insurance program for people age 65 and older, people with certain disabilities, and people with end-stage renal disease (ESRD), and has two principal parts (not including the prescription drug element begun in 2006). Medicare Part A is hospital insurance, which most Americans automatically become eligible for on their sixty-fifth birthday. Coverage under Part A does not require the payment of premiums, although there are deductible and coinsurance payments. Medicare Part B is optional medical insurance, primarily for outpatient care and doctor's services, and requires payment of monthly premiums. However, 95 percent of those eligible for Part B choose to participate. Medicaid is a state-administered health insurance program, primarily for people who are low income and for those with disabilities, that is partially financed by the federal government. Eligibility and benefits for Medicaid differ by state.

Most of the data sets discussed in this chapter contain primarily administrative data, most often evidence of medical claims paid by either the Medicaid or the Medicare system. Particularly in the case of Medicaid, therefore, researchers must be cautious about interpreting data in these files as representing the total health care needs or utilization of persons enrolled in either system because evidence of any care not paid for through the Medicaid or Medicare system would not be included in these data.

Introduction

This chapter provides a brief introduction to some basic concepts from interest rate theory and financial mathematics and applies these theories for the calculation of market values of life insurance liabilities. There exists a huge amount of literature on financial mathematics and interest rate theory, and we shall not mention all work of importance within this area. Some basic introductions are Baxter and Rennie (1996) and Hull (2005). Readers interested in more mathematical aspects of these theories are referred to Lamberton and Lapeyre (1996) and Nielsen (1999). Finally we mention Björk (1997, 2004) and Cairns (2004).

The present chapter is organized as follows. Section 3.2 demonstrates how the traditional actuarial principle of equivalence can be modified in order to deal with situations with random changes in the future interest rate, i.e. to the case of stochastic interest rates. This argument, which involves hedging via so-called zero coupon bonds, leads to new insights into the problem of determining the market value for the guaranteed payments on a life insurance contract. Section 3.3 gives a more systematic treatment of topics such as zero coupon bonds, the term structure of interest rates and forward rates. In addition, this section demonstrates how versions of Thiele's differential equation can be derived for the market value of the guaranteed payments.

Introduction

We consider in this chapter the general type of life insurance where premiums and benefits are calculated provisionally at issuance of the policy and later determined according to the performance of the insurance contract or company. The determination of premiums and benefits can take various forms depending on the type of contract. Examples are various types of participating life insurance (in some countries called with-profit life insurance) and various types of pension funding.

The determination of premiums and benefits is based on payment of dividends, which in general may be positive or negative, from the insurance company to the policy holder. It is important to distinguish between two aspects of the determination: the dividend plan and the bonus plan. The dividends plan is the plan for allocation of dividends. However, often the dividends are not paid out immediately in cash but are converted into a stream of future payments. The bonus plan is the plan for how the dividends are eventually turned into payments.

In Steffensen (2000), a framework of securitization is developed where reserves are no longer defined as expected present values but as market prices of streams of payments (which, however, happen to be expressible as expected present values under adjusted measures). An insurance contract is defined as a stream of payments linked to dynamic indices, covering a wide range of insurance contracts including various forms of unit-linked contracts.

Introduction

This chapter deals with some aspects of valuation in life and pension insurance that are relevant for accounting at market values. The purpose of the chapter is to demonstrate the retrospective accumulation of the technical reserve and to formalize an approach to prospective market valuation. We explain and discuss the principles underpinning this approach.

The exposition of the material distinguishes itself from scientific expositions of the same subject, see, for example, Norberg (2000) or Steffensen (2001). By considering firstly the retrospective accumulation of technical reserves, secondly the prospective approach to market valuation and thirdly the underpinning principles, things are turned somewhat upside down here. The aim is to meet the practical reader at a starting point with which he is familiar.

The terms prospective and retrospective play an important role. The idea of a liability as a retrospectively calculated quantity needs revision when going from the traditional composition of the liability to a market-based composition of the liability. This is an important step towards comprehending both the market-valuation approach presented here and the generalization and improvement hereof, taking into consideration more realistic actuarial and financial modeling.

Throughout the chapter, we consider all calculations pertaining to the primary example of an insurance contract. This primary example is an endowment insurance with premium intensity π, pension sum guaranteed at time 0, ba (0), and guaranteed death sum, bad. Bonus is paid out by increasing the pension sum.

Introduction

This chapter provides an introduction to life insurance practice with focus on with-profit life insurance. The purpose is to give the reader sufficient insight to benefit from the remaining chapters. In life insurance, one party, the policy holder, exchanges a stream of payments with another party, the insurance company. The exchanged streams of payments form, in a sense, the basis of the insurance contract and the corresponding legal obligations. When speaking of life insurance practice, we think of the way this exchange of payments is handled and settled by the insurer. We take as our starting point the idea of the policy holder's account. This account can be interpreted as the policy holder's reserve in the insurance company and accumulates on the basis of the so-called Thiele's differential equation. Its formulation as a forward differential equation plays a crucial role, and this chapter explains in words the construction and the elements of this equation and its role in accounting. Note, however, that the policy holder's account is not in general a capital right held by the insured but a key quantity in the insurer's handling of his obligations.

The life insurance market

In this section we explain the most typical environments for negotiation and contractual formulations for a life insurance policy. We distinguish between defined benefits and what we choose to call defined contributions with partly defined benefits.

Defined contributions with partly defined benefits cover the majority of life insurance policies.

Introduction

This chapter gives an introduction to interest rate derivatives and their use in risk-management for life insurance companies. The first part of the chapter recalls the definitions of swap rates, swaps, swaptions and related products within a setting similar to the one studied in the previous chapters. Then we describe some pricing methods that have been proposed in the literature. There are a vast number of instruments available in the financial markets, and there exist many different models for the pricing of these instruments; see, for example, Brigo and Mercurio (2001), Musiela and Rutkowski (1997) and Rebonato (2002). Our treatment of this area is rather minimal, and our aim is simply to provide a brief introduction to certain developments that seem useful in an analysis of the risk faced by life insurance companies. The reader is therefore referred to the abovementioned references for a more detailed and systematic treatment of the basic theory.

We end the chapter by giving possible applications of these instruments in the area of risk management for a life insurance company facing insurance liabilities that cannot be hedged via bonds in the market due to the very long time horizon associated with the liabilities. Typically, insurance companies are faced by insurance liabilities that extend up to sixty years into the future, whereas the financial markets typically do not offer bonds that extend more than thirty years into the future.

Introduction

In the previous chapters it has been assumed that mortality risk is diversifiable. Under this assumption, we have proposed valuation principles which could be derived by working with a big portfolio of insured lives (allowing for deterministic decrement series) or by letting the size of the portfolio converge to infinity. In Chapter 2 the financial market consisted of one single investment possibility, a risk-free asset corresponding to a savings account with a deterministic interest. Chapter 3 considered the case where the interest rate is stochastic and derived formulas for the market value of the guaranteed payments that involved the prices of zero coupon bonds. Finally, Chapter 4 studied a financial market with two investment possibilities, a stock and a savings account, and demonstrated how the market value of the total liabilities (including bonus) could be determined for fixed investment and bonus strategies. This study led to explicit formulas for the market value of the total liabilities in two specific models: the binomial model and the Black–Scholes model under the assumption of no arbitrage and diversifiable mortality risk. In this case, the market value was defined as the amount which was necessary in order to hedge the liabilities perfectly via a self-financing investment strategy.

The main goal of the present chapter is to analyze the combined, or integrated, insurance and financial risk which is present in a life insurance contract, where the benefits are linked to returns on the financial markets.

Insurance mathematics and financial mathematics have converged during the last few decades of the twentieth century and this convergence is expected to continue in the future. New valuation methods are added to the traditional valuation methods of insurance mathematics. Valuation and decision making on the asset side and the liability side of the insurance companies are, to an increasing extent, being considered as two sides of the same story.

The development has two consequences. Demands are made on practising actuaries, whose education dates back to when financial mathematics was not considered as an integrated part of insurance mathematics. By considering the convergence as it applies to their daily work, such actuaries should be kept abreast of this convergence. From this starting point, the ideas, concepts and results of finance should be brought together to construct a path between classical actuarial deterministic patterns of thinking and modern actuarial mathematics. This is where stochastic processes are brought to the surface in payment streams as well as in investment possibilities.

At the same time, present students of actuarial mathematics need to apply financial mathematics to classical insurance valuation problems. These students will typically, and should, meet financial mathematics in textbooks on pure finance. However, to receive the full benefit of financial mathematical skills, these skills need to be integrated and proven beneficial for classical problems of insurance mathematics already on a student level.

International accounting standards have developed over the years.

Introduction

In Chapter 2 we discussed some aspects of valuation assuming only one possible investment with a deterministic interest rate. In Chapter 3 we introduced a stochastic interest rate and a bond market and we discussed the consequences for valuation in general and for valuation of guaranteed payments in particular. In this chapter we again assume a deterministic interest rate, but, in return, we introduce the possibility of investing in stocks and study the total reserve including the reserve for guaranteed payments. In Section 4.6 we comment on the combination of stochastic interest rates and investment in stocks.

The total reserve in connection with a life insurance contract can, under certain conditions, be calculated using a simple retrospective accumulation. The condition is that the total reserve which has been accumulated at the termination of the contract equals the pension sum paid out. We consider the type of insurance where the surplus is accumulated in the technical reserve leading to an increasing pension sum. Here, the condition is that the undistributed reserve, which is the total reserve minus the technical reserve, at the termination of the contract equals zero. The condition and its consequences are formalized and studied in Chapter 2.

One very simple situation in Chapter 2 was the financial market, which consists of one investment possibility only, namely the possibility of investing in the risk-free interest rate. Furthermore, this risk-free interest rate is assumed to be deterministic.